Computer Science ›› 2016, Vol. 43 ›› Issue (Z11): 97-102.doi: 10.11896/j.issn.1002-137X.2016.11A.021

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t Truth Degree of Formulas and Approximate Reasoning in Gdel n-valued Propositional Logic System

ZHU Nai-diao, HUI Xiao-jing and GAO Xiao-li   

  • Online:2018-12-01 Published:2018-12-01

Abstract: By adding new operators Δ and ~,axiomatic expansion of Gdel n-valued propositional logic system is introduced,which is denoted as Gdel~,Δ.In this paper,the definition of t truth degree of propositional formula was put forward(t take Δ,~),and the MP rule,HS rule,meet and union inference rules and some related properties of t truth degree were discussed.The concepts of t similarity degree,t pseudo-metric between propositional formulas and their some related properties are obtained.Three different types of approximate reasoning patterns are introduced in logic metric space,and they are proved to be equivalent.

Key words: t truth degree,t similarity degree,t logic metric space,Approximate reasoning

[1] Pavelka J.On Fuzzy Logic I:Many-valued rules of inference[J].Mathematical Logic Quarterly,1979,5(3-6):45-52
[2] Pavelka J.On Fuzzy Logic II:Enriched residuated lattices and semantics of propositional calculi[J].Mathematical Logic Quarterly,1979,5(7-12):119-134
[3] Pavelka B J.On fuzzy logic III:Semantical completeness of some many-valued propositional calculi,Zeitschr.f.math.Logik und Grundlagen d[C]∥Math.2010
[4] 王国俊.计量逻辑学(I)[J].工程数学学报,2006,3(2):191-215
[5] 王国俊.数理逻辑引论与归结原理(第二版)[M].北京:科学出版社,2006
[6] 裴道武.基于三角模的模糊逻辑理论及其应用[M].北京:科学出版社,2013
[7] 周红军.ukasiewicz命题逻辑中命题的Borel概率真度理论和极限定理[J].软件学报,2012,3(9):2235-2247
[8] 折延宏,贺晓丽.粗糙逻辑中公式的Borel型概率粗糙真度[J].软件学报,2014,5(5):970-983
[9] 李骏,王国俊.Gdel n值命题逻辑系统中的α-真度理论[J].软件学报,2007,8(1):33-39
[10] 吴洪博.ukasiewicz命题逻辑中公式的Γ-真度理论和极限定理[J].中国科学:信息科学,2014,4:1542-1559
[11] 袁彦莉,张兴芳,李成允.n值Gdel逻辑系统中的随机化研究[J].计算机工程与应用,2010,6(12):41-45
[12] 惠小静,王国俊.经典推理模式的随机化研究及其应用[J].中国科学:E辑,2007,7(6):801-812
[13] 惠小静,王国俊.经典推理模式的随机化研究及其应用(II)[J].模糊系统与数学,2008,2(3):21-26
[14] 惠小静.三值R0命题逻辑系统的随机化[J].应用数学学报,2009,2(1):19-27
[15] 王国俊,惠小静.概率逻辑学基本定理的推广[J].电子学报,2007,5(7):1333-1340
[16] 崔美华.n值.ukasiewicz命题逻辑系统中公式的随机真度及近似推理[J].应用数学学报,2012,5(2):209-220
[17] 宋士吉,吴澄.模糊推理的反向三I算法[J].中国科学,E辑,2002,32(2):58-66
[18] 彭家寅,侯健,李洪兴.基于某些常见蕴涵算子的反向三I算法[J].自然科学进展,2005,15(4):404-410
[19] Esteva F,Godo L,Hájek P,et al.Residuated fuzzy logics with an involutive negation[J].Arch Math Logic,2000,9:103-124
[20] Flaminio T,Marchioni E.T-norm based logics with an indepen-dent an involutive negation[J].Fuzzy Set Syst,2006,7:3125-3144
[21] Baaz M.Infinite-valued Gdel logic with 0-1 projections and re-lativisations[J].Comput Sci Phys Lect Notes Logic,1996,6:23-33
[22] Cintula P,Klement E P,Mesiar R,et al.Fuzzy logics with an additional involutive negation[J].Fuzzy Set Syst,2010,1:390-411
[23] Cintula P.Weakly implicative (fuzzy) logics I:basic properties[J].Arch Math Logic,2006,45:673-704
[24] 惠小静.基于真值的SBL~公理化扩张系统的计量化[J].中国科学:信息科学,2014,4(7):900-911

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